Densities and viscosities of aqueous solutions of 1-propanol and 2-propanol at temperatures from 293.15 K to 333.15 K

Journal of Molecular Liquids 136 (2007) 71 – 78 www.elsevier.com/locate/molliq Densities and viscosities of aqueous solutions of 1-propanol and 2-propanol at temperatures from 293.15 K to 333.15 K Fong-Meng Pang a , Chye-Eng Seng a,⁎, Tjoon-Tow Teng b , M.H. Ibrahim b a b School of Chemical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia School of Industrial Technology, Universiti Sains Malaysia, 11800 Penang, Malaysia Received 26 November 2006; accepted 20 January 2007 Available online 24 February 2007 Abstract Densities and viscosities of the binary aqueous solutions of 1-propanol and 2-propanol have been measured over the whole composition range at temperatures between 293.15 K and 333.15 K. The energies of activation for viscous flow for aqueous solutions of 1-propanol and 2-propanol were calculated and found to be 17.94 and 22.16 kJ mol− 1, respectively. A polynomial equation and an equation based on the Power Law and Erying's absolute rate theory were used to correlate the viscosity data of the aqueous solutions of 1-propanol and 2-propanol. The average absolute deviations (AAD) for density correlations of aqueous solutions of 1-propanol and 2-propanol are less than 0.07%. © 2007 Elsevier B.V. All rights reserved. Keywords: Viscosity; Density; 1-propanol; 2-propanol 1. Introduction A knowledge of thermodynamic and transport properties of binary aqueous solutions is important in engineering, designing new technological processes and also in developing theoretical models. Volumetric properties of aqueous solutions, in conjunction with other thermodynamic properties provide useful information about water–solute interactions. Density and viscosity of aqueous solutions are required in both physical chemistry and chemical engineering calculations involving fluid flow, heat and mass transfer [1]. The values of such quantities may sometimes be obtained from tables but it is usually found that even the most extensive physico-chemical tables do not contain all the data necessary for designing a technological process [2]. Consequently, reliable and accurate data which can be applied to wide ranges of temperature are required. Alcohols are organic compounds widely used in the chemical industry. Main use of alcohols is solvents for gums, resins, lacquers and varnishes, in the preparation of dyes and for ⁎ Corresponding author. Tel.: +60 4 6533888x3546; fax: +60 4 6574854. E-mail address: ceseng@usm.my (C.-E. Seng). 0167-7322/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2007.01.003 essential oils in perfumery. Aqueous solutions of alcohols have served as useful industrial solvent media for a variety of separation processes. It also has become popular in solar thermal systems. Alcohols and their binary mixtures are also used as solvents in chemistry and modern technology for homogeneous and heterogeneous extractive rectification [3]. Densities and viscosities of binary aqueous solutions of 1-propanol have been studied and presented using power series equation by Mikhail and Kimel [4] at 298.15, 303.15, 308.15, 313.15 and 323.15 K. The maximum deviation of the calculated values as compared with the experimental values reported by Mikhail and Kimel was less than 0.15% and 0.88% for density and viscosity, respectively. Ling and Van Winkle [5] determined densities and viscosities of 1-propanol + water, toluene + n-octane, 1-butanol + water, acetone + 1-butanol, benzene + 2-chloroethanol, carbon tetrachloride + 1-propanol, ethanol + 1,4-dioxane and methanol + 1,4-dioxane at temperatures of 303.15, 328.15, 348.15 and 368.15 K. They found that the liquid viscosity for the same liquid composition was lower at higher temperature. Densities and refractive indices of 1-propanol, 2-propanol and methanol with water were measured at 293.15 and 298.15 K [6]. The density–composition curves for both 1-propanol 72 F.-M. Pang et al. / Journal of Molecular Liquids 136 (2007) 71–78 Table 1 Densities (ρ) and viscosities (η) of pure components at different temperatures 1-propanol 2-propanol ρ (g cm− 3) ρ (g cm− 3) η (mPa s) η (mPa s) T (K) Experiment Literature Experiment Literature Experiment Literature Experiment Literature 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 0.80428 0.80021 0.79642 0.79227 0.78851 0.78428 0.78102 0.77667 0.77282 0.80370 [10] 0.79999 [11] 0.79660 [5] 0.79200 [12] 0.78730 [4] 0.78410 [12] 0.77900 [4] 0.77610 [5] – 2.197 1.947 1.726 1.542 1.379 1.236 1.111 1.003 0.908 – 1.938 [4] 1.723 [4] 1.534 [4] 1.379 [4] 1.223 [12] 1.110 [4] 1.011 [5] – 0.78535 0.78110 0.77712 0.77288 0.76879 0.76397 0.75968 0.75489 0.75041 0.78550 [10] 0.78090 [14] 0.77680 [13] 0.77220 [15] 0.76800 [13] 0.76329 [15] 0.75930 [13] – – 2.414 2.070 1.785 1.546 1.347 1.176 1.033 0.914 0.811 – 2.052 [14] 1.780 [13] – 1.350 [13] – 1.040 [13] – – and 2-propanol exhibit a steady decrease in density with alcohol concentration. Viscosity studies of solutions of water in naliphatic alcohols were also reported at 288.15, 298.15, 308.15, and 318.15 K [7]. Densities and refractive indices of pure alcohols from 293.15 to 318.15 K were presented by Ortega [8]. Dizechi and Marschall [9] measured kinematic viscosities and densities of eight binary and four ternary liquid mixtures of polar components at various temperatures and the data were correlated with McAllister's equation and modified form of the McAllister's equation. The present study presents and discusses density and viscosity data for binary systems of 1-propanol + water and 2-propanol + water at temperatures from 293.15 K to 333.15 K over the entire composition range. The data are correlated with an equation based on the Power Law and Erying's absolute rate theory and also a polynomial type equation. 2. Experimental 2.1. Materials 1-propanol (N 99.5%) and 2-propanol (N 99.8%) were obtained from Merck Chemicals. Both were used without further purification. Ultra pure water was used for the preparation of various solutions. Mixtures of these alcohols with ultra pure water were made by weighing a known amount of the respective chemicals, taking care to minimize exposure to air (carbon dioxide). Densities and viscosities of the pure components are given in Table 1 and compared with the literature values [4,5,10–15]. this instrument was estimated to be ±1 × 10− 5 g cm− 3 and the precision of this instrument is ±0.5 × 10− 5 g cm− 3. Densities of the solutions, were calculated by the equation q ¼ A Vs2 −B V ð1Þ where A′ and B′ are calibration constants, ρ the density, τ the period of vibration. 2.3. Viscosity The kinematic viscosities of the solutions were determined by using an Ubbelohde viscometer. Ultra pure water [16] was used for calibration. The viscometer was immersed in a water bath. The temperature of the water bath was controlled to ± 0.01 K. The flow time was measured with a stop-watch accurate to ± 0.01 s. Measurements were repeated at least three times for each solution and temperature. The uncertainty of the viscosity measurements was estimated to be less than 0.4%. The kinematic viscosity of solutions is given by v ¼ k1 t−k2 =t ð2Þ where v is the kinematic viscosity, t is the flow time and k1, k2 are the viscometer constants. The values of k1 determined by calibrating with pure water at working temperatures are between 0.001753 to 0.001763 mm2 s− 2. The k2/t term represents the correction due to kinetic energy and can generally be neglected. The dynamic viscosities were then 2.2. Density An Anton Paar DMA58 vibrating tube digital density meter, with a built-in constant temperature bath was used to determine the densities of the solutions at temperatures ranging from 293.15 K to 333.15 K at 5 K intervals. The temperature of the water bath was kept constant within ±0.01 K. The density meter was calibrated by dry air and ultra pure water under atmospheric pressure. The output signal from the vibrating tube was processed through a frequency meter. The U-tube of the density meter was washed with water and acetone and dried with air before measurement. The uncertainty of Fig. 1. Viscosities of pure alcohols as a function of temperatures (●, 1-propanol; ▵, 2-propanol). 73 F.-M. Pang et al. / Journal of Molecular Liquids 136 (2007) 71–78 Table 2 Experimental viscosity for 1-propanol (1) + water (2) mixtures from 293.15 K to 333.15 K x1 0.00000 0.01000 0.02000 0.05000 0.07000 0.10000 0.20000 0.30000 0.40000 0.50000 0.60002 0.70006 0.80004 0.89997 1.00000 η (mPa s) 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 1333.15 1.002 1.156 1.335 1.898 2.209 2.545 3.109 3.173 3.053 2.880 2.707 2.537 2.403 2.300 2.197 0.890 1.024 1.160 1.603 1.844 2.116 2.598 2.674 2.592 2.465 2.333 2.202 2.097 2.022 1.947 0.797 0.906 1.019 1.366 1.555 1.786 2.192 2.267 2.216 2.118 2.023 1.920 1.839 1.783 1.726 0.719 0.810 0.912 1.187 1.342 1.530 1.879 1.953 1.915 1.840 1.765 1.686 1.623 1.581 1.542 0.653 0.728 0.807 1.039 1.167 1.330 1.625 1.692 1.666 1.610 1.547 1.485 1.437 1.405 1.379 0.596 0.659 0.726 0.919 1.027 1.164 1.420 1.479 1.460 1.416 1.366 1.315 1.278 1.254 1.236 0.547 0.600 0.657 0.820 0.912 1.030 1.250 1.303 1.288 1.252 1.212 1.171 1.142 1.123 1.111 0.504 0.551 0.599 0.738 0.817 0.920 1.112 1.157 1.146 1.117 1.084 1.050 1.026 1.012 1.003 0.466 0.507 0.549 0.669 0.738 0.827 0.994 1.034 1.024 0.999 0.971 0.944 0.925 0.914 0.908 Table 3 Experimental viscosity for 2-propanol (1) + water (2) mixtures from 293.15 K to 333.15 K x1 η (mPa s) 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 0.00000 0.01000 0.02000 0.05000 0.07069 0.10000 0.20003 0.30003 0.40003 0.50004 0.60005 0.70013 0.79990 0.89994 1.00000 1.002 1.170 1.369 2.062 2.544 3.054 3.741 3.726 3.481 3.180 2.888 2.655 2.484 2.395 2.414 0.890 1.029 1.188 1.725 2.089 2.472 3.040 3.068 2.894 2.667 2.441 2.256 2.127 2.054 2.070 0.797 0.912 1.040 1.467 1.735 2.041 2.504 2.551 2.425 2.253 2.076 1.934 1.824 1.772 1.785 0.719 0.815 0.923 1.263 1.480 1.717 2.109 2.153 2.062 1.926 1.787 1.669 1.585 1.538 1.546 0.653 0.733 0.823 1.098 1.270 1.458 1.789 1.835 1.765 1.657 1.544 1.449 1.379 1.341 1.347 0.596 0.664 0.739 0.966 1.103 1.261 1.539 1.580 1.525 1.437 1.345 1.265 1.208 1.176 1.176 0.547 0.604 0.668 0.856 0.969 1.101 1.337 1.374 1.328 1.256 1.179 1.113 1.064 1.035 1.033 0.504 0.554 0.609 0.767 0.862 0.973 1.175 1.207 1.168 1.107 1.041 0.985 0.944 0.919 0.914 0.466 0.510 0.556 0.691 0.774 0.868 1.037 1.066 1.033 0.981 0.926 0.877 0.840 0.818 0.811 Table 4 Experimental density for 1-propanol (1) + water (2) mixtures from 293.15 K to 333.15 K x1 ρ (g cm− 3) 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 0.000000 0.009998 0.019999 0.049998 0.070003 0.099997 0.200001 0.300004 0.399999 0.499996 0.600017 0.700065 0.800042 0.899968 1.00000 0.99821 0.99290 0.98848 0.97734 0.96982 0.95616 0.91803 0.89051 0.86976 0.85383 0.84071 0.82928 0.81986 0.81242 0.80428 0.99705 0.99167 0.98712 0.97534 0.96711 0.95301 0.91461 0.88665 0.86571 0.84973 0.83668 0.82512 0.81568 0.80825 0.80021 0.99565 0.99030 0.98561 0.97301 0.96417 0.95011 0.91084 0.88284 0.86162 0.84479 0.83292 0.82088 0.81142 0.80393 0.79642 0.99403 0.98859 0.98389 0.97067 0.96120 0.94679 0.90707 0.87877 0.85744 0.84047 0.82863 0.81651 0.80711 0.79987 0.79227 0.99222 0.98668 0.98187 0.96849 0.95844 0.94379 0.90341 0.87484 0.85334 0.83683 0.82373 0.81220 0.80293 0.79589 0.78851 0.99021 0.98440 0.97963 0.96629 0.95526 0.94032 0.89949 0.87111 0.84901 0.83242 0.81931 0.80774 0.79851 0.79134 0.78428 0.98804 0.98251 0.97744 0.96330 0.95252 0.93734 0.89581 0.86674 0.84482 0.82809 0.81488 0.80329 0.79421 0.78716 0.78102 0.98569 0.98019 0.97505 0.96037 0.94913 0.93371 0.89284 0.86244 0.84036 0.82359 0.81032 0.79872 0.78975 0.78270 0.77667 0.98320 0.97762 0.97243 0.95720 0.94625 0.93134 0.88786 0.85901 0.83582 0.81909 0.80567 0.79432 0.78549 0.77844 0.77282 74 F.-M. Pang et al. / Journal of Molecular Liquids 136 (2007) 71–78 Table 5 Experimental density for 2-propanol (1) + water (2) mixtures from 293.15 K to 333.15 K x1 0.00000 0.01000 0.02000 0.05000 0.07069 0.10000 0.20003 0.30003 0.40003 0.50004 0.60005 0.70013 0.79990 0.89994 1.00000 ρ (g cm− 3) 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 0.99821 0.99229 0.98735 0.97594 0.96908 0.95735 0.91714 0.88547 0.86143 0.84283 0.82745 0.81457 0.80368 0.79433 0.78535 0.99705 0.99144 0.98609 0.97412 0.96645 0.95399 0.91317 0.88129 0.85713 0.83854 0.82307 0.81020 0.79960 0.78985 0.78110 0.99565 0.98984 0.98463 0.97196 0.96244 0.95027 0.90928 0.87735 0.85292 0.83419 0.81872 0.80569 0.79464 0.78557 0.77712 0.99403 0.98816 0.98301 0.96967 0.96105 0.94670 0.90578 0.87303 0.84850 0.82956 0.81407 0.80130 0.79007 0.78101 0.77288 0.99222 0.98633 0.98117 0.96745 0.95835 0.94267 0.90120 0.86866 0.84415 0.82517 0.80951 0.79646 0.78549 0.77666 0.76879 0.99021 0.98436 0.97911 0.96549 0.95451 0.94081 0.89695 0.86419 0.83950 0.82048 0.80479 0.79166 0.78072 0.77192 0.76397 0.98804 0.98207 0.97724 0.96201 0.95152 0.93826 0.89361 0.85988 0.83511 0.81611 0.80015 0.78704 0.77614 0.76748 0.75968 0.98569 0.97992 0.97518 0.95898 0.94861 0.93444 0.89000 0.85528 0.83038 0.81124 0.79520 0.78210 0.77118 0.76296 0.75489 0.98320 0.97750 0.97192 0.95656 0.94828 0.93304 0.88444 0.85095 0.82584 0.80649 0.79001 0.77701 0.76635 0.75791 0.75041 calculated from the measured kinematic viscosities and the densities of the same solutions. where A is a system specific constant, E the activation energy for viscous flow, R the gas constant and T the temperature in Kelvin. Plots of ln η versus 1/T for pure 1-propanol and 2-propanol are shown in Fig. 1. The values of E, the activation energies for viscous flow, of 1-propanol and 2-propanol were found to be 17.94 and 22.16 kJ mol− 1 with the correlation coefficient N0.9999. 2-propanol has higher activation energy than 1-propanol probably due to the larger structure of 2-propanol in resisting flow. The alcohol aggregates become more bulky and flow less easily as the structure of alcohol becomes larger. Extra energy is required to break the hydrogen bond in the secondary alcohols. For pure alcohols, the temperature dependence of the viscosity becomes stronger with increasing degree of branching. The viscosity is higher for branched alcohols than for the n-alcohol at low temperature, whereas the viscosity decreases faster for the branched alcohols than for the n-alcohol as the temperature increases. This temperature dependent behavior may follow from the fact that at low temperatures the association of branched Fig. 2. Viscosities of 1-propanol (1) + water (2) systems from 293.15 K to 333.15 K (●, this work; □, Mikhail and Kimel [4]; ▴, Ling and Van Winkle [5]; , D'Aprano et al. [7]). Fig. 3. Viscosities of 2-propanol (1) + water (2) systems from 293.15 K to 333.15 K (●, this work; □, Mato and Coca [18]; ▵, Taniewska-Osinska and Kacperska [19]). 3. Results and discussion Numerous empirical and theoretical equations have been formulated to relate the variations of viscosity with temperature, pressure and the bulk and structural properties of the liquids. Most notable among the empirical equations used is the Andrade equation which relates viscosity, η and absolute temperature, T, by an Arrhenius type of exponential function g ¼ A exp ðE=RT Þ ▪ ð3Þ 75 F.-M. Pang et al. / Journal of Molecular Liquids 136 (2007) 71–78 Table 6 Parameters ai of Eq. (4) for viscosity of binary aqueous 1-propanol solutions T (K) a1 a2 a3 a4 a5 a6 AAD% 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 0.9596 0.8630 0.7765 0.7060 0.6396 0.5849 0.5372 0.4959 0.4595 22.6495 17.7274 14.1008 11.4701 9.5088 7.9519 6.7379 5.7924 5.0183 −81.8479 −61.8624 −47.7885 −37.9942 −30.9668 −25.4952 −21.3787 −18.3139 −15.8049 131.6387 96.7569 72.9931 56.9090 45.7326 37.1016 30.7748 26.3534 22.5812 − 101.9294 −73.2237 −54.0813 −41.4093 −32.8468 −26.2406 −21.4783 −18.4052 −15.5771 30.7325 21.6902 15.7279 11.8616 9.3123 7.3335 5.9183 5.0807 4.2315 1.012 0.738 0.608 0.425 0.466 0.437 0.407 0.404 0.374 Table 7 Parameters ai of Eq. (4) for viscosity of binary aqueous 2-propanol solutions T (K) a1 a2 a3 a4 a5 a6 AAD% 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 0.8965 0.8196 0.7487 0.6844 0.6279 0.5769 0.5316 0.4928 0.4574 30.1282 22.9893 17.8859 14.2991 11.4858 9.4385 7.8640 6.6220 5.6529 − 109.5571 −81.1228 −61.7891 −48.5914 −38.2748 −31.1384 −25.7806 −21.5074 −18.4286 171.6818 123.8812 92.8855 72.0433 55.6804 44.8530 36.9080 30.3646 26.2088 −128.8869 −90.9939 −67.4918 −51.7182 −39.2663 −31.3040 −25.5914 −20.6715 −18.0311 38.1523 26.4963 19.5456 14.8290 11.0930 8.7498 7.1009 5.6131 4.9519 1.917 1.477 1.147 0.930 0.737 0.626 0.554 0.470 0.437 alcohol molecules is stronger whereas, as temperature increases, the branched alcohols become more monomolecular like than linear alcohols [17]. The experimental viscosities and densities data for the binary aqueous solutions of 1-propanol and 2-propanol from 293.15 K to 333.15 K are presented in Tables 2–5, respectively. The viscosities of the aqueous solutions of 1-propanol and 2-propanol are plotted versus mole fraction in Figs. 2 and 3. The literature viscosity data of aqueous 1-propanol [4,5,7] are also plotted in Fig. 2 for comparison. The viscosities of 1-propanol measured in this work are in good agreement with the available literature data [4,5,7], except for the viscosity values at 298.15 K reported by D' Aprano et al. [7], which are slightly higher at high mass fraction of 1-propanol. The literature viscosity data of aqueous 2-propanol [18,19] are also plotted in Fig. 3 for comparison. The measured aqueous 2-propanol data also agree well with those available data [18,19]. Tables 2 and 3 show that viscosity values decrease with temperature. For both the binary systems, viscosity increases with the mole fraction of alcohol, reaching a weak maximum at about 0.3000 mol fraction of alcohol, beyond which the viscosity decreases slowly due to strong interactions between water and alcohol. Two equations are proposed to correlate the viscosity of the aqueous solutions of 1-propanol and 2-propanol systems i.) Polynomial equation [20]: g ¼ g0 þ 6 X ai x i ð4Þ i¼1 where η is the viscosity of the binary solutions, η0 the viscosity of pure water at the same temperature, ai are the polynomial coefficients. Eq. (4) was used to fit the experimental data. The best-fit values of the polynomial coefficients are listed in Tables 6 and 7. ii.) Equation based on the Power Law and Erying's absolute rate theory [21]: An equation for liquid viscosity has been derived based on the Power Law equation for non-Newtonian fluid equation and Erying's absolute rate theory. The equation for a concentration Table 8 Parameters of Eq. (5) for viscosity of binary aqueous 1-propanol solutions T (K) 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 E′ V ψ2 ψ12 β σ (s) AAD% 1.1731 8.9237 0.8822 5.3900 3.7406 32.7667 1.398 1.1382 8.5430 0.8902 5.0102 3.7775 29.6323 1.088 1.1300 8.2256 0.9044 4.9037 3.7988 27.7891 0.908 1.1004 7.9922 0.9095 4.5506 3.8208 25.1850 0.682 1.1014 7.7804 0.9231 4.5578 3.8470 23.9903 0.695 1.0969 7.6242 0.9335 4.4949 3.8606 22.5868 0.608 1.0987 7.5580 0.9435 4.4698 3.8732 21.2379 0.555 1.1006 7.4248 0.9498 4.4372 3.8452 20.1432 0.528 1.1018 7.4021 0.9569 4.3959 3.8371 18.9129 0.482 76 F.-M. Pang et al. / Journal of Molecular Liquids 136 (2007) 71–78 Table 9 Parameters of Eq. (5) for viscosity of binary aqueous 2-propanol solutions T (K) 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 E′ V ψ2 ψ12 β σ (s) AAD% 1.1195 9.6951 0.9176 6.4924 5.0262 34.5774 2.122 1.0967 9.3122 0.9151 5.8999 4.6997 30.4144 1.807 1.0723 8.9873 0.9113 5.2857 4.6046 27.3282 1.608 1.0563 8.7079 0.9174 5.0203 4.5349 25.1252 1.358 1.0275 8.4304 0.9227 4.6394 4.5014 23.0022 1.107 1.0240 8.2195 0.9304 4.5410 4.4112 21.5665 0.954 1.0236 8.0680 0.9387 4.4792 4.3256 20.2460 0.834 1.0162 7.8994 0.9445 4.3664 4.2620 19.0483 0.677 1.0148 7.7074 0.9487 4.2804 4.1381 18.0365 0.649 dependent binary system viscosity is obtained using additive contribution from each component. g ¼ ðsc =rc Þ½ðg0 =sc ÞexpðxE VÞ=ð1 þ xV ފÞWc ð5Þ where, ψC = 1 − x β + x β (1 − x β )ψ12 + x β ψ2 and σc = σ ψc− 1 η is viscosity of the binary solutions, τc is shear stress, σc is the apparent viscosity rates, x is mole fraction, E′ is activation energy of viscous flow, V is molar volume of holes, subscripts 1 and 2 denote components 1 and 2 in the binary system, subscript 12 denotes a non-linear constant for the binary system and β is a non-linear adjustable constant for mole fraction. Eq. (5) was used to fit the experimental data with the MATLAB program. The best-fit parameters are listed in Tables 8 and 9. It is noted that all parameters are dimensionless except for σ which has a dimension of seconds (s). The activation energy E′ is the difference between the molar free energy of activation for creating holes in the liquid by moving particle of pure component 1 and component 2. E V¼ ðDG⁎2 −DG⁎1 Þ=RT ð6Þ where ΔG⁎ is the free activation energy constant, R is the gas constant and T is the temperature. Decreasing E′ with temperature, it indicates that the rate of decrease of the molar free energy of activation for creating holes in the liquid of pure component 2 is slower than that of pure component. Tables 8 and 9 show that the values of E′ decrease with increasing temperatures for 1-propanol and 2-propanol systems. The molar volume of holes, V is found gradually decreasing with temperature. A decrease in V parameter indicates that the solute molar volume of holes expands slower than its solvent with temperature. The molar volume of holes can be expressed as V ¼ ðV2 −V1 Þ=V1 where ND is the total number of data in the sample, subscript exptl denotes experimental data and subscript calc denotes calculated value. The polynomial equation correlates the viscosity with an AAD of 0.541% and 0.922%, respectively, for 1-propanol and 2-propanol aqueous solution systems. The Power Law and Erying's absolute rate theory correlate the viscosity values of the binary solutions with an AAD of 0.771% and 1.235% for 1-propanol and 2-propanol aqueous systems, respectively. The density data for the binary aqueous solutions of 1-propanol and 2-propanol are shown in Figs. 4 and 5. The literature density data of aqueous 1-propanol solution [4,5] are included in Fig. 4 for comparison. The measured density data are in good agreement with those in the literature. The density data of 2-propanol aqueous solutions reported by Sakurai [15] and TaniewskaOsinska and Kacperska [19], are included in Fig. 5. The measured aqueous 2-propanol data are found to be in good agreement with the literature data [15,19]. Density is a function of temperature and composition for aqueous solutions. Thus from Tables 4 and 5, the densities generally decrease with temperature and composition of alcohol. Densities for binary solutions can be represented by the ð7Þ where subscripts 1 and 2 denote components 1 and 2 in the binary system. The ψ2 value increases with temperature. The parameter β is an adjustable parameter. It represents how the non-Newtonian deviation constant changes with concentration for a binary system. The overall regression results are measured using average absolute percent deviation (AAD) AAD% ¼ 1=ND X ½ðgexptl −gcalc Þ=gexptl Þ2 Š1=2  100% ð8Þ Fig. 4. Densities of 1-propanol (1) + water (2) systems from 293.15 K to 333.15 K (●, this work; □, Mikhail and Kimel [4]; ▴, Ling and Van Winkle [5]). 77 F.-M. Pang et al. / Journal of Molecular Liquids 136 (2007) 71–78 Table 11 Coefficients of Eq. (9) for density of binary aqueous 2-propanol solutions Fig. 5. Densities of 2-propanol (1) + water (2) systems at various temperatures (●, this work; □, Sakurai [15]; ▴, Taniewska-Osinska and Kacperska [19]). following polynomial equation which is convenient for interpolation [22] d ¼ d0 þ 5 X ai x i ð9Þ i¼1 where d0 is the density of pure water at the temperature concerned, ai are the temperature dependence polynomial coefficients, and x is the mole fraction of the alcohols. At a given temperature, the signs of ai depend on the magnitude of molar mass of the solute and multiplication of d0 with apparent molal volume ∅v. For solutes whose molar masses are smaller than d0∅v, like acetone and some alcohols a1 will be negative [23]. The polynomial coefficients are listed in Tables 10 and 11. The average absolute deviation (AAD) for density calculations are 0.068% and 0.066%, respectively, for aqueous 1-propanol and 2-propanol systems. 4. Conclusions The densities and viscosities of aqueous 1-propanol and 2-propanol solutions have been measured over the entire Table 10 Coefficients of Eq. (9) for density of binary aqueous 1-propanol solutions T (K) a1 a2 a3 a4 a5 AAD% 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 −0.4398 −0.4673 −0.4900 −0.5157 −0.5344 −0.5524 −0.5650 −0.5787 −0.5863 0.1140 0.2174 0.2852 0.3870 0.4580 0.5198 0.5374 0.5889 0.5876 0.8571 0.6682 0.5736 0.3721 0.2272 0.1182 0.1321 0.0172 0.0540 − 1.2230 − 1.0598 − 1.0009 − 0.8109 − 0.6702 − 0.5792 − 0.6288 − 0.5056 − 0.5572 0.4981 0.4450 0.4330 0.3657 0.3157 0.2875 0.3170 0.2689 0.2912 0.083 0.076 0.065 0.067 0.070 0.071 0.065 0.057 0.060 T (K) a1 a2 a3 a4 a5 AAD% 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 − 0.4074 − 0.4392 − 0.4716 − 0.4951 − 0.5221 − 0.5275 − 0.5264 − 0.5483 − 0.5490 −0.1371 −0.0275 0.1087 0.1875 0.2783 0.2335 0.1705 0.2621 0.1935 1.2831 1.1036 0.8391 0.7033 0.5625 0.7301 0.9119 0.7070 0.9371 −1.5256 −1.3853 −1.1545 −1.0405 −0.9422 −1.1401 −1.3359 −1.1203 −1.3952 0.5756 0.5334 0.4606 0.4242 0.4004 0.4781 0.5519 0.4689 0.5811 0.078 0.065 0.057 0.044 0.058 0.064 0.072 0.066 0.092 concentration range at temperatures from 293.15 to 333.15 K. 2-propanol has higher activation energy than 1-propanol. 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